This invention relates generally to electric circuits that generate a voltage larger than a supply voltage from which they operate by the switching of charge along serial capacitive cells, known as charge pumps.
A well known charge pump is the Dickson charge pump, which is shown in FIG. 1. As described by Louie Pylarinos of the University of Toronto in “Charge Pumps: An Overview”, the circuit has two pumping clocks which are anti-phased and have a voltage amplitude of Vφ or {overscore (Vφ)}. Serial diodes or diode connected NMOSFETS, D1–D4, operate as self-timed switches characterized by a forward biased voltage, Vt, which is the threshold voltage of each diode. Each diode has a stray capacitance, Cs, associated therewith. The charge pump operates by pumping charge along the diode chain as capacitors C1–C4 are successively charged and discharged during each clock cycle. For example, when Vφ goes high, diode D1 conducts and the voltage at its anode, V1, is boosted by voltage Vφ and transferred to node V2 less a voltage drop, Vt, associated with diode D1. Then when Vφ goes low, and {overscore (Vφ)} goes high, the charge at node V2 is transferred to node V3 less a voltage drop, Vt, associated with diode V2. After N stages, it is seen that the output voltage isVout=Vin+N·(Vφ−Vd)−Vd  (1)The stray capacitance, Cs, can be taken into account by noticing that it reduces the transferred clock voltage, Vφ, by a factor
      C          C      +              C        s              .Thus, the actual output voltage becomes
                              V          out                =                              V            in                    +                      N            ·                          (                                                                    (                                          C                                              C                        +                                                  C                          s                                                                                      )                                    ·                                      V                    ϕ                                                  -                                  V                  d                                            )                                -                      V            d                                              (        2        )            
Until now is has been assumed that no load was connected to the output of the charge pump. In the presence of such a load which draws a current, lout, the output voltage is reduced by an amount
            N      ·              I        out                            (                  C          +                      C            s                          )            ·              f        osc              ,where fosc is the operating frequency of the charge pump. The output voltage now becomes
                              V          out                =                              V            in                    +                      N            ·                          (                                                                    C                                          C                      +                                              C                        s                                                                              ·                                      V                    ϕ                                                  -                                  V                  d                                -                                                      I                    out                                                                              (                                              C                        +                                                  C                          s                                                                    )                                        ·                                          f                      osc                                                                                  )                                -                      V            d                                              (        3        )            From this equation it becomes apparent that the voltage multiplication will occur only if
                                                        C                              C                +                                  C                  s                                                      ·                          V              ϕ                                -                      V            d                    -                                    I              out                                                      (                                  C                  +                                      C                    s                                                  )                            ·                              f                osc                                                    >        0                            (        4        )            Following Dickson, eq (3) can be written as
                              V          out                =                  Vo          -                                                    I                out                            ·                              R                s                                      ⁢                                                  ⁢            where                                              (        5        )                                Vo        =                              V            in                    -                      V            d                    +                                    N              ·                              (                                                                            C                                              C                        +                                                  C                          s                                                                                      ·                                          V                      ϕ                                                        -                                      V                    d                                                  )                                      ⁢                                                  ⁢            and                                              (        6        )                                          R          s                =                  N                      C            +                                          C                s                            ·                              f                osc                                                                        (        7        )            Equation (3) leads to an equivalent circuit of the charge pump as shown in FIG. 2.
Limitations of the Dickson charge pump when implemented with NMOS transistors or diode connected transistors lies in the trapped charge associated with each node due to the threshold voltage, Vt, of each NMOS diode. While increasing capacitor charge reduces effective series resistance, Rs, there is a practical limitation of capacitor size in an integrated circuit. While clock frequency, fosc, reduces series resistance, the charge must be able to be transferred from node to node within a cycle, otherwise increasing frequency will not improve pump performance.